Problem: Simplify the following expression: $\sqrt{45} + \sqrt{125}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{45} + \sqrt{125}$ $= \sqrt{9 \cdot 5} + \sqrt{25 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{5} + \sqrt{25} \cdot \sqrt{5}$ $= 3\sqrt{5} + 5\sqrt{5}$ Finally, simplify by combining the terms. $= ( 3 + 5 )\sqrt{5} = 8\sqrt{5}$